X-Alignment Techniques for
Improving the Observability of
Response Compactors
Ozgur Sinanoglu
Sobeeh Almukhaizim†
Math & Computer Science Department
Kuwait University
ozgur@sci.kuniv.edu.kw
Computer Engineering Department
Kuwait University
sobeeh@eng.kuniv.edu.kw
2010년 10월 16일
김인수
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Purposes of this paper
• Improving the observability of response
compactors.
• Enhancing fault detection per test pattern.
• Making room for more test patterns in the
tester memory.
– Propose X-Align technique.
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Properties of X-alignment techniques
• X-alignment hardware is fixed for a given design
and is independent of any test set and any fault
model.
• X-alignment hardware can be reconfigured based
on any given set of test responses.
• X-alignment techniques can be utilized in
conjunction with any response compactor to
manipulate x-distribution in favor of the
compactor
• X-alignment hardware has a small area overhead
and its insertion can be seamlessly integrated into
the conventional design flow.
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Response compaction techniques
Vertical Compaction Methods
Horizontal Compaction Methods
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XOR-based V-compaction
• XOR-based compaction with two parity trees
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XOR-based V-compaction with V-align
• Delaying shift-out operations in two scan chains for aligning x’s
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XOR-based V-compaction with V-align
•
Vertical Align block
ΔMAX (maximum allowable delay) = 3
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Vertical Alignment of X’s
the transformation of the scan response into a map of known and unknown bits.
T(c, δ) := 1 if(δ − 1)th cell of cth chain = x,
0 otherwise
0 ≤ c < num_chains, 1 ≤ δ ≤ depth
the definition of the solution variables.
dc := 1 if cth chain is delayed,
0 otherwise
0 ≤ c < num_chains
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Vertical Alignment of X’s
Slices :
if the scan slice i is observable:
: AND clause
s0 = (d0 + d0) ∧ (d1 + d1) ∧ (0 + d2) ∧ (d3 + d3) = d2
s1 = d1 ∧ d2 ∧ d3
s2 = d0 ∧ d1 ∧ d2 ∧ d3
s3 = 0
s4 = d0
d0 = d2 = 1, d1 = d3 = 0
s1 = s4 = 1, s0 = s2 = s3 = 0
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XOR-based H-compaction with H-align
• Horizontal Align block
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Horizontal Alignment of X’s
the rotation of scan slices into a map of known and unknown bits.
T(c, δ) := 1 if δth cell of cth chain = x,
0 otherwise
does not increase the scan depth
0 ≤ c < num_chains, 0 ≤ δ ≤ depth
the definition of the rotation variables.
rδ := 1 if δth chain is rotated,
0 otherwise
rotate direction : upward
0 ≤ δ ≤ depth
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Horizontal Alignment of X’s
if the scan chain i is observable:
Chains:
: AND clause
c0 = (r0 + r0) ∧ (r1) ∧ (r2) ∧ (r3) = r1 ∧ r2 ∧ r3
c1 = r0 ∧ r1 ∧ r2
c2 = r0 ∧ r1 ∧ r2
c3 = r1 ∧ r2 ∧ r3
r1 = 1, r0 = r2 = r3 = 0
c1 = c3 = 1, c0 = c2 = 0
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2D-alignment
• Vertical Alignment
• Horizontal Alignment
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2D-alignment
Without Alignment
(Obs = 0)
With v-align Only
(Obs = 6)
With h-align Only
(Obs = 8)
With v-align After h-Align
(Obs = 10)
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2D-alignment
• A clear advantage of aligning x’s in both
directions (regardless of the order) is that
the observability level of the 2Dalignment is guaranteed to surpass, or
be equal to, that when x’s are aligned in
one direction only.
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Response Shaper
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X-Alignment: Random Responses
# of observable scan cells
Px : unknown probability
ΔMAX = 1
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X-Alignment: Industrial Responses
# of observable scan cells
A, B : two industrial circuits(provided by Cadence)
80X196 : 80 scan chains with a scan depth of 196
ΔMAX = 1
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COST COMPARISONS ON ISCAS89 CIRCUITS
20 CHAINS, SINGLE XOR TREE
TDV : Test data volume of the base case includes those of uncompressed stimuli and
uncompacted responses.
The reported area costs for x-align and response shaper do not include the cost of the XOR
tree.
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